Multiplicative Inverses of Matrices and Matrix Equations

1. Find the products AB and BA to determine whether B is a multiplicative inverse of A (similar to p.603 #2)

2. Find the products AB and BA to determine whether B is a multiplicative inverse of A (similar to p.603 #6)

3. Use the following fact: to find the inverse of each matrix, if possible. Check that the matrix you find is the inverse. (similar to p.603 #14)

5. Find A-1 by forming [A|I] and then using row operations to obtain [I|B] where A-1 = [B]. Check that AA-1 = I and A-1A = I (similar to p.603 #24)

6. Write each linear system as a matrix equation in the form AX = B where A is the coefficient matrix and B is the constant matrix (similar to p.604 #30)

8. Write each matrix equation as a system of linear equations without matrices (similar to p.604 #34)

9. a) Write each linear system as a matrix equation in the form AX = B 9. a) Write each linear system as a matrix equation in the form AX = B. b) Solve the system using the inverse that is given for the coefficient matrix. (similar to p.604 #38)